On certain classes of rectangular designs

TL;DR

This paper classifies rectangular designs into various classes, introduces matrix-based construction methods for selfdual and alpha-resolvable designs, and explores their combinatorial and statistical significance.

Contribution

It presents a novel matrix approach to construct and classify rectangular designs, including selfdual and alpha-resolvable types, expanding the methods for design construction.

Findings

Constructed new series of selfdual designs

Developed matrix methods for design classification

Linked designs to automorphisms and statistical applications

Abstract

Rectangular designs are classified as regular, Latin regular, semiregular, Latin semiregular and singular designs. Some series of selfdual as well as alpharesolvable designs are obtained using matrix approaches which belong to the above classes. In every construction we obtain a matrix N whose blocks are square (0,1) matrices such that N becomes the incidence matrix of a rectangular design. The method is the reverse of the well known tactical decomposition of the incidence matrix of a known design. Authors have already obtained some series of Group Divisible and Latin square designs using this method. Tactical decomposable designs are of great interest because of their connections with automorphisms of designs, see Bekar et al. (1982). The rectangular designs constructed here are of statistical as well as combinatorial interest.